(k)=[e(k,02(k)…,O(k be the jth chromosome. Note that earlier we had concatenated elements in a string while here we simply take the concatenated elements and form a vector from then). We do this simply because this is probably the way that you will want to code the algorithm in the computer. We will at times, however, still let aj be a concatenated string when it is onvenient to do se The population of individuals at time k is given by P(k)={0(k)j=12……S} and the number of individuals in the population is given by S. We want to pick S to be big enough so that the population elements can cover the search space. However, we do not want S to be too big since this increases the number of computations we have to perform Genetic Operations The population P(k at time k is often referred to as the"generation"of individuals at time k. Evolution occurs as we go from a generation at time k to the next generation at time k+1. Genetic operations of selection, crossover, and mutation are used to produce one generation from the next. Selection: Basically, according to Darwin the most qualified individuals survive to mate. We quantify"most qualified via an individual's fitness J (e, (k )at time k. For selection we create a"mating pool"at time k, which we denote by M(k)={m(k) The mating pool is the set of chromosomes that are selected for mating. We select an individual for mating by tting each m k)be equal to 0(k)eP(k) with probability P J((k) ∑。J(0(k) To clarify the meaning of this formula and hence the selection strategy, Goldberg [58]uses the analogy of spinning a unit circumference roulette wheel where the wheel is cut like a pie into S regions where the ith region is associated with the ith element of P(k). Each preshaped region has a portion of the circumference that is given by, in Equation(4.7) You spin the wheel, and if the pointer points at region i when the wheel stops, then you place 0 into the mating pool M(k). You spin the wheel S times so that 5 elements end up in the mating pool. Clearly, individuals who are more fit will end up with more copies in the mating pool; hence, chromosomes with larger-than-average fitness will embody a greater portion of the next generation. At the same time, due to the probabilistic nature of the selection process, it is possible that some relatively unfit individuals may end up in the mating pool PDF文件使用" pdffactory Pro"试用版本创建ww. fineprint,com,cn1 2 ( ) [ ( ), ( ), , ( )] j j j j T N q k = q k q q k k  be the jth chromosome. Note that earlier we had concatenated elements in a string while here we simply take the concatenated elements and form a vector from then). We do this simply because this is probably the way that you will want to code the algorithm in the computer. We will at times, however, still let θj be a concatenated string when it is convenient to do so. The population of individuals at time k is given by ( ) { ( ) | 1, 2, ,S} j P k = = q k j …… (4.5) and the number of individuals in the population is given by S. We want to pick S to be big enough so that the population elements can cover the search space. However, we do not want S to be too big since this increases the number of computations we have to perform. Genetic Operations The population P(k) at time k is often referred to as the "generation" of individuals at time k. Evolution occurs as we go from a generation at time k to the next generation at time k+1. Genetic operations of selection, crossover, and mutation are used to produce one generation from the next. Selection: Basically, according to Darwin the most qualified individuals survive to mate. We quantify "most qualified" via an individual's fitness J k (q j ( )) at time k. For selection we create a "mating pool" at time k, which we denote by ( ) { ( ) | 1, 2, ,S} j M k = = m k j …… (4.6) The mating pool is the set of chromosomes that are selected for mating. We select an individual for mating by letting each mj(k) be equal to ( ) ( ) j q k Î P k with probability 1 ( ( )) ( ( )) i i S j j J k P J k q q = = å (4.7) To clarify the meaning of this formula and hence the selection strategy, Goldberg [58] uses the analogy of spinning a unit circumference roulette wheel where the wheel is cut like a pie into S regions where the ith region is associated with the ith element of P(k). Each pieshaped region has a portion of the circumference that is given by, in Equation (4.7). You spin the wheel, and if the pointer points at region i when the wheel stops, then you place i q into the mating pool M(k). You spin the wheel S times so that 5 elements end up in the mating pool. Clearly, individuals who are more fit will end up with more copies in the mating pool; hence, chromosomes with larger-than-average fitness will embody a greater portion of the next generation. At the same time, due to the probabilistic nature of the selection process, it is possible that some relatively unfit individuals may end up in the mating pool. PDF 文件使用 "pdfFactory Pro" 试用版本创建 www.fineprint.com.cn